Question: Simplify; express your answer in exponential form. Assume $q\neq 0, p\neq 0$. $\dfrac{{(q^{2})^{-5}}}{{q^{4}p^{3}}}$
Answer: To start, try working on the numerator and the denominator independently. In the numerator, we have ${q^{2}}$ to the exponent ${-5}$ . Now ${2 \times -5 = -10}$ , so ${(q^{2})^{-5} = q^{-10}}$ In the denominator, we can use the distributive property of exponents. ${q^{4}p^{3} = q^{4}p^{3}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(q^{2})^{-5}}}{{q^{4}p^{3}}} = \dfrac{{q^{-10}}}{{q^{4}p^{3}}}$ Break up the equation by variable and simplify. $\dfrac{{q^{-10}}}{{q^{4}p^{3}}} = \dfrac{{q^{-10}}}{{q^{4}}} \cdot \dfrac{{1}}{{p^{3}}} = q^{{-10} - {4}} \cdot p^{- {3}} = q^{-14}p^{-3}$.